Convert degrees to radians
Converting degrees to radians is a common angle task, whether you are checking a recipe, a spec sheet, a travel distance or a homework problem. Since 1 ° equals 0.0174533 rad, the math is a single multiplication — and this page does it for you instantly, with the formula, a table of common values and answers to the questions people ask most.
Exact factor
How to convert degrees to radians
To convert degrees to radians, multiply the number of degrees by 0.0174533. For example, 10 ° × 0.0174533 = 0.174533 rad.
rad = ° × 0.0174533
- Write down the value in degrees you want to convert.
- Multiply it by 0.0174533 (the exact °→rad factor).
- The result is your value in radians. Check it below with the converter or the table.
Conversion table
Common values of degrees and their equivalents in radians:
| ° | rad |
|---|---|
| 1 | 0.0174533 |
| 2 | 0.0349066 |
| 3 | 0.0523599 |
| 4 | 0.0698132 |
| 5 | 0.0872665 |
| 10 | 0.174533 |
| 20 | 0.349066 |
| 25 | 0.436332 |
| 50 | 0.872665 |
| 100 | 1.74533 |
| 250 | 4.36332 |
| 500 | 8.72665 |
About these units
Degree (°). A degree is 1/360 of a full circle, the everyday angle unit inherited from Babylonian astronomy. Maps, compasses, geometry classes and weather use degrees.
Radian (rad). A radian is the angle subtended by an arc equal in length to the radius, with π radians in a half circle (about 57.2958°). It is the natural angle unit in mathematics and programming.
Frequently asked questions
How do I convert degrees to radians?
To convert degrees to radians, multiply the number of degrees by 0.0174533. For example, 10 ° × 0.0174533 = 0.174533 rad. Or skip the math: type the value into the converter at the top of this page and the result updates instantly.
How many radians are in 1 degree?
1 ° = 0.0174533 rad. That is the fixed relationship used by this converter and by international standards.
How many degrees are in 1 radian?
1 rad = 57.2958 °. If you are converting in the opposite direction, use our Radian to Degree converter for the dedicated table and FAQ.
Is the degrees to radians conversion exact?
Yes. Both units are defined by international agreement, so the factor of 0.0174533 is exact. Displayed results are rounded to 6 significant digits only for readability.
What is degree used for?
A degree is 1/360 of a full circle, the everyday angle unit inherited from Babylonian astronomy. Maps, compasses, geometry classes and weather use degrees.